2.13.1 Solving Rational Inequalities

Question 1

rational inequality

Answer 1

an inequality that contains one or more rational expressions

Question 2

Steps for Solving a Rational Inequality

Answer 2

1. Set the rational expression in relation to 0.
2. Find the critical values. A. Set the numerator equal to 0 and solve to find the x-value where the inequality is equal to 0. B. Set the denominator equal to 0 and solve to find the x-value where the inequality is undefined.
3. Mark the critical values on a number line, dividing it into regions.
4. Choose a random value from one of these regions on the number line and test that value in the inequality
   (substitute the value into the inequality for x and simplify). If the result is true, then that entire region is part of the inequality’s solution. Repeat for each region on the number line.
5. Write the solution using inequalities or interval notation.